scholarly journals Lattice Hamiltonian approach to the massless Schwinger model: Precise extraction of the mass gap

2013 ◽  
Vol 184 (7) ◽  
pp. 1666-1672 ◽  
Author(s):  
Krzysztof Cichy ◽  
Agnieszka Kujawa-Cichy ◽  
Marcin Szyniszewski
Keyword(s):  
Hamiltonian Approach ◽  
Schwinger Model ◽  
Mass Gap

scholarly journals Lattice Hamiltonian approach to the Schwinger model

2015 ◽  
Author(s):  
Marcin Szyniszewski ◽  
Krzysztof Cichy ◽  
Agnieszka Kujawa-Cichy
Keyword(s):  
Hamiltonian Approach ◽  
Schwinger Model

scholarly journals Anomalies and renormalization of mixed states in quantum theories

2014 ◽  
Vol 29 (13) ◽  
pp. 1450064 ◽  
Author(s):  
Kumar S. Gupta ◽  
Amilcar de Queiroz
Keyword(s):  
Moduli Space ◽  
Time Reversal ◽  
Condensed Matter ◽  
Quantum Spin ◽  
Hamiltonian Approach ◽  
Mixed States ◽  
Expectation Values ◽  
Quantum Theories ◽  
Long Wavelength ◽  
Mass Gap

In a Hamiltonian approach to anomalies, parity and time-reversal symmetries can be restored by introducing suitable impure (or mixed) states. However, the expectation values of observables such as the Hamiltonian diverges in such impure states. Here, we show that such divergent expectation values can be treated within a renormalization group (RG) framework, leading to a set of β-functions in the moduli space of the operators representing the observables. This leads to well-defined expectation values of the Hamiltonian in a phase where the impure state restores the P and T symmetry. We also show that this RG procedure leads to a mass gap in the spectrum. Such a framework may be relevant for long wavelength descriptions of condensed matter systems such as the quantum spin Hall (QSH) effect.

Light front field theory: An advanced Primer

2007 ◽  
Vol 57 (3) ◽  
Author(s):  
L'ubomír Martinovič
Keyword(s):  
Field Theory ◽  
Detailed Comparison ◽  
Light Front ◽  
Two Dimensional ◽  
Schwinger Model ◽  
Initial Space ◽  
Model Hamiltonian ◽  
Spatial Volume ◽  
Hamiltonian Perturbation Theory ◽  
Light Front Quantization

Light front field theory: An advanced PrimerWe present an elementary introduction to quantum field theory formulated in terms of Dirac's light front variables. In addition to general principles and methods, a few more specific topics and approaches based on the author's work will be discussed. Most of the discussion deals with massive two-dimensional models formulated in a finite spatial volume starting with a detailed comparison between quantization of massive free fields in the usual field theory and the light front (LF) quantization. We discuss basic properties such as relativistic invariance and causality. After the LF treatment of the soluble Federbush model, a LF approach to spontaneous symmetry breaking is explained and a simple gauge theory - the massive Schwinger model in various gauges is studied. A LF version of bosonization and the massive Thirring model are also discussed. A special chapter is devoted to the method of discretized light cone quantization and its application to calculations of the properties of quantum solitons. The problem of LF zero modes is illustrated with the example of the two-dimensional Yukawa model. Hamiltonian perturbation theory in the LF formulation is derived and applied to a few simple processes to demonstrate its advantages. As a byproduct, it is shown that the LF theory cannot be obtained as a "light-like" limit of the usual field theory quantized on an initial space-like surface. A simple LF formulation of the Higgs mechanism is then given. Since our intention was to provide a treatment of the light front quantization accessible to postgradual students, an effort was made to discuss most of the topics pedagogically and a number of technical details and derivations are contained in the appendices.

Path integrals and the solution of the Schwinger model in curved space-time

1986 ◽  
Vol 33 (8) ◽  
pp. 2262-2266 ◽  
Author(s):  
J. Barcelos-Neto ◽  
Ashok Das
Keyword(s):  
Path Integrals ◽  
Space Time ◽  
Curved Space ◽  
Schwinger Model

scholarly journals Passive Guaranteed Simulation of Analog Audio Circuits: A Port-Hamiltonian Approach

2016 ◽  
Vol 6 (10) ◽  
pp. 273 ◽  
Author(s):  
Antoine Falaize ◽  
Thomas Hélie
Keyword(s):  
Hamiltonian Approach

scholarly journals Hamiltonian Approach to Magnetic Fields with Toroidal Surfaces

1985 ◽  
Vol 40 (10) ◽  
pp. 959-967
Author(s):  
A. Salat
Keyword(s):  
Magnetic Field ◽  
Hamiltonian System ◽  
Magnetic Fields ◽  
Constant Pressure ◽  
Time Dependent ◽  
Hamiltonian Approach ◽  
One Dimensional ◽  
Mhd Equilibrium ◽  
Magnetic Surfaces ◽  
Rotational Transform

The equivalence of magnetic field line equations to a one-dimensional time-dependent Hamiltonian system is used to construct magnetic fields with arbitrary toroidal magnetic surfaces I = const. For this purpose Hamiltonians H which together with their invariants satisfy periodicity constraints have to be known. The choice of H fixes the rotational transform η(I). Arbitrary axisymmetric fields, and nonaxisymmetric fields with constant η(I) are considered in detail.Configurations with coinciding magnetic and current density surfaces are obtained. The approach used is not well suited, however, to satisfying the additional MHD equilibrium condition of constant pressure on magnetic surfaces.

scholarly journals Critical behavior of the 2d scalar theory: resumming the N8LO perturbative mass gap

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Gustavo O. Heymans ◽  
Marcus Benghi Pinto
Keyword(s):  
Perturbation Theory ◽  
Critical Behavior ◽  
State Of The Art ◽  
Critical Coupling ◽  
Scalar Theory ◽  
Perturbative Series ◽  
Supercritical Region ◽  
Mass Gap ◽  
Perturbative Result ◽  
Symmetric Phase

Abstract We apply the optimized perturbation theory (OPT) to resum the perturbative series describing the mass gap of the bidimensional ϕ4 theory in the ℤ2 symmetric phase. Already at NLO (one loop) the method is capable of generating a quite reasonable non-perturbative result for the critical coupling. At order-g7 we obtain gc = 2.779(25) which compares very well with the state of the art N8LO result, gc = 2.807(34). As a novelty we investigate the supercritical region showing that it contains some useful complimentary information that can be used in extrapolations to arbitrarily high orders.

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